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Introduction to number theory. (English) Zbl 0651.10001

Wiley-Interscience Publication. New York etc.: Wiley. xii, 212 p. £27.50 (1989).
This is a textbook for an advanced undergraduate or beginning graduate course introducing to number theory. The chapters treat prime numbers and unique factorization, sums of two squares, quadratic reciprocity, indefinite binary quadratic forms and class groups and genera of binary quadratic forms. So the emphasis is on Diophantine equations (especially quadratic equations in two variables, which are treated to some depth) ending with a proof of Gauß’ three squares theorem.
An appendix A is a reprint of a lecture of J.-P. Serre with the title “\(\Delta =b^2-4ac\)” [Math. Medley 13, 1–10 (1985; Zbl 0596.12004)], concerning recent developments on class numbers \(h(\Delta)\) up to the Gross-Zagier theorem, an appendix B consists of tables of prime numbers and class numbers. Hundreds of exercises are scattered throughout the text, sometimes extending the theory.
This is a self-contained well-written introduction concentrating on topics from Gauß’ Disquisitiones Arithmeticae.

MSC:

11-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory
11Axx Elementary number theory
11Dxx Diophantine equations
11Exx Forms and linear algebraic groups
11E41 Class numbers of quadratic and Hermitian forms

Citations:

Zbl 0596.12004
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